Differential Equations and Linear Algebra - Math 2250
Fall 2013 - Sect 10 (11/12)
Lectures:
Labotary:
MTWF 10:45am-11:35am - WEB L110
H 9:40am-10:30am - JWB 333 - Section 11
H 10:45am-11:35am - LCB 121 - Section 12
Instructor:
Christel Hohenegger
Office:
LCB 333
Phone:
(801) 585-1637
E-mail:
choheneg@math.utah.edu
Webpage:
http://www.math.utah.edu/~choheneg
TA:
Jenna Noll - LCB 313 - noll@math.utah.edu
Course webpage: Canvas on CIS (http://cis.utah.edu)
Office Hours:
TBD or by appointment
Textbook: Differential Equations and Linear Algebra With Introductory Partial Differential Equations and Fourier Series (Custom Edition for the University of Utah), by
C. Henry Edwards, David E. Penney, and Richard Haberman; PEARSON Learning
Solutions, 2013; ISBN-13: 978-1-269-42557-5; price is about $195.
Updates: Topics covered and assignments are listed at the end of the syllabus. However,
the weekly schedule is subject to change during the semester depending on the lectures.
Updated topics and assignments will be posted on Canvas. You are responsible for
checking it regularly.
http://utah.instructure.com/courses/245426
Mathematics Tutoring Center: Free tutorial is available in room 155 of the T.
Benny Rushing Mathematics Center (adjacent to the LCB and JWB). Hours are 8am8pm Monday-Thursday and 8am-6pm on Friday. There is also a computer lab in the
Rushing Student Center. You all have Math Department computer accounts by virtue
of being enrolled in a Math class and may print related material for free. For more
information consult the website.
http://www.math.utah.edu/ugrad/mathcenter.html
You might find the videos and problems from the website of the Khan Academy helpful.
https://www.khanacademy.org/
The math department has videos available online of the lower level calculus classes up
to Calculus II (MATH 1010, MATH 1050, MATH 1060, MATH 1210 and MATH 1220).
http://www.math.utah.edu/lectures/
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College of Engineering Tutoring Lab: Additional office hours held by the TAs for
the engineering calculus sequence (MATH 1310, MATH 1311, MATH 1320, MATH 1321)
and MATH 2250 will be scheduled in WEB 1622. Hours are 8am-5pm Monday-Thursday.
TAs hours will be posted once the schedule is determined.
Prerequisites: ”C” or better in MATH 2210, or MATH 1260, or MATH 1280, or
MATH 1321, or MATH 1320, or (MATH 1220, or MATH 1250, or MATH 1270, or
MATH 1311), or AP Calculus BC score of 5 AND (PHYS 2210, or PHYS 3210). singlevariable calculus.) You are also expected to have learned about vectors and parametric
curves (Math 2210, 1260, 1280, or Physics 2210 or 3210). Practically speaking, you are
expected to have learned about single-variable calculus, vectors and parametric curves.
Description: The course will cover essential of knowledge of differential equations and
linear algebra used for engineering applications. The course is structured into four lecture
hours per week, and one lab hour per week. The lecture class will incorporate instructor
lectures, including content on the applications to Engineering, weekly short quizzes and
random pop quizzes. Lab sections will comprise group problem solving sessions led by
the teaching assistant, weekly homework discussion and students participation. The goal
of Math 2250 is to master the basic tools and problem solving techniques important in
differential equations and linear algebra. The work you will complete in Math 2250
comprises weekly homework and quizzes, three super quizzes, two midterm exams, and
a comprehensive final exam. Homework will be turned in and quizzes will be given every
Friday except during exam days and holidays.
Learning Objectives:
• Be able to model dynamical systems that arise in science and engineering, by
using general principles to derive the governing differential equations or systems
of differential equations. These principles include linearization, compartmental
analysis, Newtons laws, conservation of energy and Kirchoffs law.
• Learn solution techniques for first order separable and linear differential equations. Solve initial value problems in these cases. Understand how to approximate
solutions even when exact formulas do not exist.
• Visualize solution and approximations to initial value problems via slope fields.
• Become fluent in matrix algebra techniques, in order to be able to compute the
solution space to linear systems and understand its structure; by hand for small
problems and with technology for large problems.
• Be able to use the basic concepts of linear algebra such as linear combinations,
span, independence, basis and dimension to understand the solution space to linear
equations and linear (system of) differential equations.
• Understand the natural initial value problems for first order systems of differential
equations, and how they encompass the natural initial value problems for higher
order differential equations and general systems of differential equations.
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• Learn how to solve constant coefficient linear differential equations via superposition, particular solutions, and homogeneous solutions found via characteristic
equation analysis. Apply these techniques to understand the solutions to the basic
unforced and forced mechanical and electrical oscillation problems.
• Learn how to use Laplace transform to solve linear differential equations, with an
emphasis on the initial value problems of mechanical and electrical systems.
• Be able to find eigenvalues and eigenvectors for square matrices. Apply these
matrix algebra concepts to find the general solution space to first and second
order constant coefficient homogeneous linear systems of differential equations,
especially those arising from compartmental analysis and mechanical systems.
• Understand and be able to use linearization as a technique to understand the
behavior of nonlinear autonomous dynamical systems near equilibrium solutions.
Apply these techniques to non-linear mechanical oscillation problems and other
systems of two first order differential equations, including interacting populations.
Relate the phase portraits of non-linear systems near equilibria to the linearized
data, in particular to understand stability.
• Develop your ability to communicate modeling and mathematical explanations and
solutions, using technology and software such as Maple, Matlab.
Problem solving fluency:
• You will be able to read and understand problem descriptions, then be able to formulate equations modeling the problem usually by applying geometric or physical
principles. You will be able to select the appropriate solution methods, execute
them accurately, and interpret the results.
• You will also gain experience with problem solving in groups. You should be able to
effectively transform problem objectives into appropriate problem solving methods
through collaborative discussion. You will also learn how to articulate questions
effectively with both the instructor and TA, and be able to effectively convey how
problem solutions meet the problem objectives.
Reading: You are expected to have read the corresponding section prior to each class.
We will cover about three sections per week. Even if you spend as little as ten minutes
on this, it will make the discussion in class much clearer, and overall you will save time.
Attendance to the lab is mandatory and will be recorded. You should attend all the
lectures, however attendance will not be checked in lectures. Remember that homework,
quizzes, super quizzes and exams happen during lectures on Fridays.
Lab: Every Thursday a Teaching Assistant-directed lab section will be held. These lab
sections have smaller class sizes allowing the TA to closely monitor students learning.
In lab, the TA will hand out problem worksheets and will facilitate student-led group
work. The worksheet problems will provide guided practice with both basic methods, as
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well as longer in-depth problems with physical and engineering applications. Credit will
be given for both lab attendance and completed worksheets. You should expect that
worksheets will take additional time outside of lab to finish completely. Lab worksheets
will be turned in the following Thursday. The lowest two worksheet scores will be
dropped. The group work will also help the students prepare for the homework, quizzes,
and exams given the subsequent Friday. Please attend the lab session you registered for.
Quizzes: At the end of every Friday class (except when an exam or super quiz is
scheduled), a short 1-2 problem quiz will be given, taking roughly 10 minutes. The quiz
will cover relevant topics covered in the week’s lectures and in the lab section. The
lowest quiz score will be dropped. No make-up quiz will be given.
Super Quizzes: Two weeks prior to each exam, a more extensive quiz will be given, consisting of 3-5 problems and taking roughly 30 minutes to complete. The super quiz will
cover material from the preceding weeks. The lowest super quiz score will be dropped.
Check with the up-to-date Canvas schedule for the dates of the super quizzes. The
tentative dates are September 20, November 1, December 6.
Homework: Roughly three textbook sections are due every Friday at the end of class
(except when there is an exam, when homework is collected on the following Monday),
based on lecture sections covering through the preceding Wednesday. Assigned problems
are listed on Canvas only. The assignments may be updated dynamically through the
course, so be sure to check Canvas regularly to see the specific problems due each week.
About two problems per section will be randomly selected for grading. The lowest three
homework scores will be dropped. Only hardcopy assignments will be accepted (no
digital copies) and no late homework will be accepted.
Midterm exams: There will be two in-class exams (55 minutes). No books, notes,
formula sheets, calculators (scientific or not), computers, phones (smart or not) or electronic device will be allowed. The tentative dates are: October 4, November 15.
Always consult Canvas to confirm those dates. None of the exams can be dropped. You
can replace the score of your lowest exam by the score of the final exam (if better).
Review and practice: A practice exam will be posted a week prior to the midterm
with problems drawn from the same material. Review of the practice exam will occur
both in lecture and in the lab section.
Final Exam: The two-hour final exam is comprehensive. It will be held on Friday
December 20, 10:30am-12:30pm.
Review and practice: As with the midterms, a practice final will be posted a week
prior and we will have a review session before the final (TBD).
Make-up and regrading: Any conflict leading to missed exams or super quizzes are
your responsibility and must be arranged ahead of time or within a week past the test.
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Failure to do so may result in a zero for the corresponding test. Regrading inquiries
must be submitted in writing within a week of the test being returned.
Students with Disabilities: The University of Utah seeks to provide equal access
to its programs, services and activities for people with disabilities. If you will need
accommodations in the class, reasonable prior notice needs to be given to the Center for
Disability Services, 162 Olpin Union Building, 581-5020. CDS will work with you and
us to make arrangements for accommodations.
Grading: Grades are determined as a weighted average as follows
Lab Worksheets
5%
15%
Quizzes Super Quizzes
5%
5%
Homework Exams Final
10%
30%
30%
Letter grades A/B/C/D are determined as follows 100/85/70/55. I reserve the right to
modify these in special cases and to decide if a curve is needed.
Honor Code: You are expected to abide by the University of Utah Honor Code and to
avoid any instances of academic misconduct, including but not limited to: (1) possessing,
using, or exchanging improperly acquired written or oral information during an exam,
(2) substitution of material that is wholly or substantially identical to that created or
published by another individual(s), and (3) false claims of performance or work.
Strategies for success:
• Attend class and lab. Being engaged helps you learn.
• Plan to do homework daily.
• Missing quizzes and homework will affect your grade. Know when the super quizzes
and exams are. Know how grades are computed before its too late.
• Form study groups with other students. Working in groups helps students selfevaluate what they know and what they do not know.
• Cramming does not work. Instead study steadily during the semester. Focus on
understanding the material rather than memorizing formulae.
• Read all the problems before you start working on any of them. Check your
answers and make sure they are correct and well presented.
Jenna and I want you to be successful, not only in this class, but in your entire undergraduate career and we are here to help you. Do not be shy to ask questions during and
after lectures, to come by office hours or to email us with any concerns.
Have a great semester !
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